Arnold's potentials and quantum catastrophes II
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00558300" target="_blank" >RIV/61389005:_____/22:00558300 - isvavai.cz</a>
Nalezeny alternativní kódy
RIV/62690094:18470/22:50019585
Výsledek na webu
<a href="https://doi.org/10.1016/j.aop.2022.168896" target="_blank" >https://doi.org/10.1016/j.aop.2022.168896</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aop.2022.168896" target="_blank" >10.1016/j.aop.2022.168896</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Arnold's potentials and quantum catastrophes II
Popis výsledku v původním jazyce
In paper I (Znojil, 2020) it has been demonstrated that besides the well known use of the Arnold's one-dimensional polynomial potentials V-(k)(x) = x(k+1) + c(1)x(k-1) + ... in the classical Thom's catastrophe theory, some of these potentials (viz., the confining ones, with k = 2N + 1) could also play an analogous role of genuine benchmark models in quantum mechanics, especially in the dynamical regime in which N + 1 valleys are separated by N barriers. For technical reasons, just the ground states in the spatially symmetric subset of V-(k)(x) = V-(k)(-x) have been considered. In the present paper II we will show that and how both of these constraints can be relaxed. Thus, even the knowledge of the trivial leading-order form of the excited states will be shown sufficient to provide a new, truly rich level-avoiding spectral pattern. Secondly, the fully general asymmetric-potential scenarios will be shown tractable perturbatively.
Název v anglickém jazyce
Arnold's potentials and quantum catastrophes II
Popis výsledku anglicky
In paper I (Znojil, 2020) it has been demonstrated that besides the well known use of the Arnold's one-dimensional polynomial potentials V-(k)(x) = x(k+1) + c(1)x(k-1) + ... in the classical Thom's catastrophe theory, some of these potentials (viz., the confining ones, with k = 2N + 1) could also play an analogous role of genuine benchmark models in quantum mechanics, especially in the dynamical regime in which N + 1 valleys are separated by N barriers. For technical reasons, just the ground states in the spatially symmetric subset of V-(k)(x) = V-(k)(-x) have been considered. In the present paper II we will show that and how both of these constraints can be relaxed. Thus, even the knowledge of the trivial leading-order form of the excited states will be shown sufficient to provide a new, truly rich level-avoiding spectral pattern. Secondly, the fully general asymmetric-potential scenarios will be shown tractable perturbatively.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Annals of Physics
ISSN
0003-4916
e-ISSN
1096-035X
Svazek periodika
442
Číslo periodika v rámci svazku
JUL
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
15
Strana od-do
168896
Kód UT WoS článku
000804940000003
EID výsledku v databázi Scopus
2-s2.0-85130175974